maximum-modulus theorem
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Maximum modulus principle — A plot of the modulus of cos(z) (in red) for z in the unit disk centered at the origin (shown in blue). As predicted by the theorem, the maximum of the modulus cannot be inside of the disk (so the highest value on the red surface is somewhere… … Wikipedia
maximum principle — Math. the theorem that a function of a complex variable that is analytic in a domain and on its boundary attains its maximum absolute value on the boundary. Also called maximum modulus principle. * * * … Universalium
maximum principle — Math. the theorem that a function of a complex variable that is analytic in a domain and on its boundary attains its maximum absolute value on the boundary. Also called maximum modulus principle … Useful english dictionary
Carlson's theorem — In mathematics, in the area of complex analysis, Carlson s theorem is a uniqueness theorem about a summable expansion of an analytic function. It is typically invoked to defend the uniqueness of a Newton series expansion. Carlson s theorem has… … Wikipedia
Open mapping theorem (complex analysis) — In complex analysis, the open mapping theorem states that if U is a connected open subset of the complex plane C and f : U → C is a non constant holomorphic function, then f is an open map (i.e. it sends open subsets of U to open subsets of… … Wikipedia
Borel–Carathéodory theorem — In mathematics, the Borel–Carathéodory theorem in complex analysis shows that an analytic function may be bounded by its real part. It is an application of the maximum modulus principle. It is named for Émile Borel and Constantin Carathéodory.… … Wikipedia
Perron–Frobenius theorem — In linear algebra, the Perron–Frobenius theorem, proved by Oskar Perron (1907) and Georg Frobenius (1912), asserts that a real square matrix with positive entries has a unique largest real eigenvalue and that the corresponding… … Wikipedia
Chinese remainder theorem — The Chinese remainder theorem is a result about congruences in number theory and its generalizations in abstract algebra. In its most basic form it concerned with determining n, given the remainders generated by division of n by several numbers.… … Wikipedia
Damodar Dharmananda Kosambi — D. D. Kosambi Born July 31, 1907 Kosben, Goa Died June 29, 1966 Pune, Maharashtra Occupation Mathematician and Marxist h … Wikipedia
List of mathematics articles (M) — NOTOC M M estimator M group M matrix M separation M set M. C. Escher s legacy M. Riesz extension theorem M/M/1 model Maass wave form Mac Lane s planarity criterion Macaulay brackets Macbeath surface MacCormack method Macdonald polynomial Machin… … Wikipedia
Riemann zeta function — ζ(s) in the complex plane. The color of a point s encodes the value of ζ(s): dark colors denote values close to zero and hue encodes the value s argument. The white spot at s = 1 is the pole of the zeta function; the black spots on the… … Wikipedia
